I have the same problem, well almost the same - although the tap is closed, the water keeps running. Plumber fixed it and soon as he left the tap went back to being broken. It's not a washer problem.
You might have to take the entire tap apart and make adjustments on the inside in order to make it work normal.
These taps are difficult to service !!! When the washer deteriorates it loses its friction and should be replaced, Personally though think it is just as easy to replace the tap head. Reason been the difficulty of changing the washer and little chance of success, and its only about a �10 more to replace it. So it is not even worth trying to repair.